Question

practice & problem solving
leveled practice in 7 - 9, find the area of each figure.
7.
8.
total area = area of parallelogram + area of trapezoid
total area = area of rhombus + area of triangle
=( 7cdotsquare+\frac{1}{2}cdot(square + 5)cdotsquare )
=( squarecdotsquare+\frac{1}{2}cdotsquarecdotsquare )
=( square + 28 )
=( square+square )
=( square ft^{2} )
=( square in.^{2} )
the total area is ( square ) square feet.
the total area is ( square ) square inches.
9.
area of original figure = area of
=( squarecdotsquare )
=( square yd^{2} )
the total area is ( square ) square feet.

1. michelle is laying carpet

in her hallway

a. choose efficient methods michelle wants to decompose her hallway into the fewest number of
quadrilaterals possible. what shapes will she decompose it into?
b. how many square feet of carpet does michelle need?

Explanation:

Step1: Solve for problem 7

Calculate the area of the parallelogram

The formula for the area of a parallelogram is \(A = base\times height\). Here, the base of the parallelogram is \(7\) ft and the height is \(2\) ft. So, \(A_{parallelogram}=7\times2\).

Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{1}{2}(a + b)h\), where \(a\) and \(b\) are the lengths of the parallel sides and \(h\) is the height. Here, \(a = 7\) ft, \(b = 5\) ft, and \(h=4\) ft. So, \(A_{trapezoid}=\frac{1}{2}(7 + 5)\times4\).

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Step2: Solve for problem 8

Calculate the area of the rhombus

The area of a rhombus (which can be considered as a parallelogram in terms of area formula \(A = base\times height\)). Here, base \(b = 14\) in and height \(h = 6\) in. So, \(A_{rhombus}=14\times6\).

Calculate the area of the triangle

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 14\) in and \(h = 6\) in. So, \(A_{triangle}=\frac{1}{2}\times14\times6\).

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Step3: Solve for problem 9

The original figure can be transformed (by moving the non - shaded parts) into a parallelogram. The base of the parallelogram is \(7\) yd and the height is \(4\) yd. Using the formula \(A = base\times height\), \(A = 7\times4=28\).

Step4: Solve for problem 10a

A rectangle and a trapezoid. A rectangle is a quadrilateral with four right angles (\(90^{\circ}\)) and opposite sides equal. A trapezoid is a quadrilateral with one pair of parallel sides.

Step5: Solve for problem 10b

Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). The rectangle has length \(l=8\) ft and width \(w = 3\) ft. So, \(A_{rectangle}=8\times3\).

Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{1}{2}(a + b)h\). Here, \(a=(10 - 3)=7\) ft, \(b=(8)\) ft, and \(h=(5 - 3)=2\) ft.

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Answer:

1. The total area is \(38\) square feet.
2. The total area is \(126\) square inches.
3. The total area is \(28\) square yards.

10a. Rectangle and trapezoid.
10b. Michelle needs \(39\) square feet of carpet.